Measurement library optimization in semiconductor metrology

ABSTRACT

Methods and systems for optimizing a set of measurement library control parameters for a particular metrology application are presented herein. Measurement signals are collected from one or more metrology targets by a target measurement system. Values of user selected parameters of interest are resolved by fitting a pre-computed measurement library function to the measurement signals for a given set of library control parameters. Values of one or more library control parameters are optimized such that differences between the values of the parameters of interest estimated by the library based measurement and reference values associated with trusted measurements of the parameters of interest are minimized. The optimization of the library control parameter values is performed without recalculating the pre-computed measurement library. Subsequent library based measurements are performed by the target measurement system using the optimized set of measurement library control parameters with improved measurement performance.

CROSS REFERENCE TO RELATED APPLICATION

The present application for patent is a continuation of, and claimspriority under 35 U.S.C. § 120 from, U.S. patent application Ser. No.15/184,782, entitled “Measurement Library Optimization In SemiconductorMetrology,” filed Jun. 16, 2016, which, in turn, claims priority under35 U.S.C. § 119 from U.S. provisional patent application Ser. No.62/180,517, entitled “Maximum Likelihood Based Optimization Frameworkfor Library-based Critical Dimensions Measurement in SemiconductorProcess,” filed Jun. 16, 2015, the subject matter of which isincorporated herein by reference in its entirety.

TECHNICAL FIELD

The described embodiments relate to metrology systems and methods, andmore particularly to methods and systems for improved measurementaccuracy.

BACKGROUND INFORMATION

Semiconductor devices such as logic and memory devices are typicallyfabricated by a sequence of processing steps applied to a specimen. Thevarious features and multiple structural levels of the semiconductordevices are formed by these processing steps. For example, lithographyamong others is one semiconductor fabrication process that involvesgenerating a pattern on a semiconductor wafer. Additional examples ofsemiconductor fabrication processes include, but are not limited to,chemical-mechanical polishing, etch, deposition, and ion implantation.Multiple semiconductor devices may be fabricated on a singlesemiconductor wafer and then separated into individual semiconductordevices.

Optical metrology processes are used at various steps during asemiconductor manufacturing process to detect defects on wafers topromote higher yield. Optical metrology techniques offer the potentialfor high throughput without the risk of sample destruction. A number ofoptical metrology based techniques including scatterometry andreflectometry implementations and associated analysis algorithms arecommonly used to characterize critical dimensions, film thicknesses,composition and other parameters of nanoscale structures.

As devices (e.g., logic and memory devices) move toward smallernanometer-scale dimensions, characterization becomes more difficult.Devices incorporating complex three-dimensional geometry and materialswith diverse physical properties contribute to characterizationdifficulty.

In response to these challenges, more complex optical tools have beendeveloped. Multiple, different measurement technologies are available,and measurements are performed over a large ranges of several machineparameters (e.g., wavelength, azimuth and angle of incidence, etc.), andoften simultaneously. As a result, the measurement time, computationtime, and the overall time to generate reliable results, including thesynthesis of measurement libraries, increases significantly.

Library based measurements employ one or more pre-computed functionalmodels that relate values of parameters of interest to measurement data(e.g., spectra). The pre-computed functional model approximates thesolution of Maxwell's equations for a given set of parameter values. Thelibrary is synthesized from training data prepared by theoreticalanalysis and calculation of subsystem configuration, signalsensitivities, geometric models, etc. The process of building ameasurement library is expensive in time and computational effort.

In many instances, the measurement library is validated based onmeasured reference data. Reference measurement data is typicallycollected from trusted measurement instruments, such as a transmissionelectron microscope, a scanning electron microscope, an atomic forcemicroscope, scanning tunneling microscope, an x-ray based metrologysystem, etc., and the results are compared with estimates provided bythe measurement library.

Typically, the estimates provided by the measurement library do notmatch the reference data within specified margins for early measurementlibrary iterations. The synthesis of the measurement library often doesnot involve a significant amount of real fabrication process knowledge.This leads to modeling inaccuracies in early measurement libraryiterations that must be corrected. Thus, additional effort must beexpended to study the root cause, modify the geometric model, andregenerate the library. This results in a substantial loss of time andcomputational effort. In addition, measured reference data is typicallyavailable only at the very late stages of a development cycle. Thus, thedelays associated with library regeneration have a significant impact ofproduction schedules.

As the available range of optical metrology measurement subsystems andassociated recipes has increased, so has the complexity of themeasurement selection process. Improved methods and tools to optimizethe use of precomputed library functions to perform accurate librarybased measurements are desired.

SUMMARY

Methods and systems for optimizing a set of measurement library controlparameters for a particular metrology application are presented herein.The metrology application includes the measurement of structural andmaterial characteristics (e.g., material composition, dimensionalcharacteristics of structures and films, etc.) associated with differentsemiconductor fabrication processes.

In one aspect, the library control parameters are optimized such thatdifferences between reference measurements of one or more parameters ofinterest of one or more metrology targets and estimated values of theparameters of interest are minimized. Measurement signals (e.g.,measured spectra) are collected by a target measurement system from thesame metrology target(s) measured by the reference metrology system. Theestimated values of the parameters of interest are resolved by fitting apre-computed measurement library function to the measurement signals fora given set of library control parameters. In some embodiments, thevalues of the library control parameters are iteratively evolved until acost function that characterizes the differences between referencemeasurements and estimated values of the parameters of interest passes apredetermined threshold value. Importantly, the optimization of thelibrary control parameter values is performed without recalculating thepre-computed measurement library.

In a further aspect, the optimized set of measurement library controlparameters is subsequently employed by the target measurement system toperform measurements of similar targets using the same measurementlibrary, but with optimized library control parameter values. In thismanner, improved measurement performance is achieved withoutregenerating the measurement library.

In another further aspect, a maximum likelihood based approach isemployed to arrive at library control parameter values that increase theaccuracy of library based measurements (e.g., critical dimensionmeasurements). The maximum likelihood based approach efficientlyoptimizes the library control parameter values to improve the fittingquality of the library measurement to reference measurement data withoutregenerating the measurement library. This approach significantlyreduces the development time necessary to achieve satisfactorymeasurement accuracy for a given metrology application.

In some embodiments, the reference measurement data is generated by atrusted reference measurement system, such as a transmission electronmicroscope, a scanning electron microscope, an atomic force microscope,a scanning tunneling microscope, an x-ray based metrology system, or anycombination thereof.

In some embodiments, the library control parameters include measurementsubsystem combination weights, measurement signal weights, one or morespecimen parameters fixed to specific values, one or more constraints onfloating parameter values, or any combination thereof.

The target measurement system may include many different measurementsystem configurations such as a spectroscopic ellipsometerconfiguration, a spectroscopic reflectometer configuration, asingle-wavelength ellipsometer configuration, a single wavelengthreflectometer configuration, a beam profile ellipsometer configuration,a beam profile reflectometer configuration, or any combination thereof.

The foregoing is a summary and thus contains, by necessity,simplifications, generalizations and omissions of detail; consequently,those skilled in the art will appreciate that the summary isillustrative only and is not limiting in any way. Other aspects,inventive features, and advantages of the devices and/or processesdescribed herein will become apparent in the non-limiting detaileddescription set forth herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrative of a system 100 for measuringcharacteristics of a semiconductor wafer in accordance with the methodsdescribed herein.

FIG. 2 is a diagram illustrative of an exemplary automated measurementlibrary control parameter optimization (AMLCPO) tool 150 implemented bycomputing system 130 depicted in FIG. 1.

FIG. 3 depicts a plot 165 of estimated values and correspondingreference values of a parameter of interest.

FIG. 4 depicts a diagram of a metrology target 170 to be measured, forexample, by measurement system 100 depicted in FIG. 1. Geometricparameters of interest include critical dimension (CD) offsets A-E.

FIGS. 5A-5C depict tables 171-173, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for ten different weightingsamong four different measurement system combinations.

FIGS. 6A-6C depict tables 174-176, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for eleven differentweightings among three different measurement system combinations.

FIGS. 7A-7C depict tables 177-179, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for eight differentweightings between two different measurement system combinations.

FIG. 8 illustrates a method 200 for optimizing library control parametervalues for a particular metrology application in at least one novelaspect.

DETAILED DESCRIPTION

Reference will now be made in detail to background examples and someembodiments of the invention, examples of which are illustrated in theaccompanying drawings.

Model based optical measurement of critical dimensions (CDs), thin filmthicknesses, optical properties and material compositions, overlay,lithography focus/dose, etc., typically requires a geometric model ofthe underlying structure to be measured. Thus, a measurement modelincludes the physical dimensions, material properties, andparameterization of the structure. In some embodiments, the measurementmodel is constructed from a file that contains equations representativeof the geometric features of the structure to be measured. In someembodiments, this file is generated by a lithography simulator such asPROLITH software available from KLA-Tencor Corporation, Milpitas, Calif.(USA). The measurement model sets the parameterization and constraintsof the measurement model based on this application information.

The measurement model includes machine parameter values and specimenparameter values that depend on the particular measurement system andmetrology target under consideration. In one example, the SpectraShape™10K metrology tool available from KLA-Tencor, Corporation, Milpitas,Calif. (USA), offers three different angles of incidence, an arbitraryselection of azimuth angle, selectable wavelength range, and more thanone collection angle. Such a metrology tool offers a wide range ofmeasurement subsystem options (e.g., spectroscopic ellipsometry andspectroscopic reflectometry) and measurement signal options. Each ofthese options may be particularly sensitive to some geometric parametersof the metrology target and not particularly sensitive to others.

In a library generation phase, a measurement library is generated basedon a set of training data derived from simulations of a particularmeasurement scenario. Typically, an electromagnetic system modelcorresponding to the particular measurement system configuration andmetrology target(s) under measurement is simulated. In some embodiments,the measurement library is a neural network model trained on the set oftraining data. The trained measurement library is a fast mathematicalapproximation of the solution of the simulated electromagnetic systemfor a given set of model parameter values. In a measurement phase, theprecomputed measurement library is employed to estimate parameter valuesfrom measured data (e.g., measured spectra) by recursion. Morespecifically, an iterative fitting procedure is employed to fitmeasurement data predicted by the library based on estimated modelparameter values to actual measurement data. The estimated modelparameter values include the parameters of interest under measurement(e.g., critical dimensions, film thicknesses, etc.).

During the measurement phase, a number of library control parametersdictate the configuration of the measurement library itself and how theprecomputed measurement library handles measured data provided to thelibrary. Library control parameters are selectable without regeneratingthe measurement library. Thus, selection of library control parametervalues affects library based measurement results without libraryregeneration. Library control parameters include, but are not limitedto, measurement subsystem combination weights, measurement signalweights, fixed parameter values, and constraints on floating parametervalues, etc. Due to the increased number of measurement subsystemoptions and measurement signal options, and the increased complexity ofmetrology targets, an automated and systematic approach to the selectionof library control parameter values is important.

Methods and systems for optimizing a set of measurement library controlparameters for a particular metrology application are presented herein.The metrology application includes the measurement of structural andmaterial characteristics (e.g., material composition, dimensionalcharacteristics of structures and films, etc.) associated with differentsemiconductor fabrication processes. The optimization of the librarycontrol parameters minimizes differences between reference measurementdata collected from one or more metrology targets by a referencemetrology system and measurement signals (e.g., measured spectra)collected from the same metrology target(s) by a target metrology systemthat employs the measurement library. The optimized set of measurementlibrary control parameters is subsequently employed by the targetmeasurement system to perform measurements of similar targets using thesame measurement library. In this manner, improved measurementperformance is achieved without regenerating the measurement library.

In one aspect, a maximum likelihood based approach is employed to arriveat library control parameter values that increase the accuracy oflibrary based measurements (e.g., critical dimension measurements). Themaximum likelihood based approach efficiently optimizes the librarycontrol parameter values to improve the fitting quality of the librarymeasurement to reference measurement data without regenerating themeasurement library. This approach significantly reduces the developmenttime necessary to achieve satisfactory measurement accuracy for a givenmetrology application.

FIG. 1 illustrates a system 100 for measuring characteristics of asemiconductor wafer. As shown in FIG. 1, the system 100 may be used toperform spectroscopic ellipsometry measurements of one or morestructures 114 of a semiconductor wafer 112 disposed on a waferpositioning system 110. In this aspect, the system 100 may include aspectroscopic ellipsometer 101 equipped with an illuminator 102 and aspectrometer 104. The illuminator 102 of the system 100 is configured togenerate and direct illumination of a selected wavelength range (e.g.,120-1700 nm) to the structure 114 disposed on the surface of thesemiconductor wafer 112. In turn, the spectrometer 104 is configured toreceive light from the surface of the semiconductor wafer 112. It isfurther noted that the light emerging from the illuminator 102 ispolarized using a polarization state generator 107 to produce apolarized illumination beam 106. The radiation reflected by thestructure 114 disposed on the wafer 112 is passed through a polarizationstate analyzer 109 and to the spectrometer 104. The radiation receivedby the spectrometer 104 in the collection beam 108 is analyzed withregard to polarization state, allowing for spectral analysis ofradiation passed by the analyzer. These spectra 111 are passed to thecomputing system 116 for analysis of the structure 114.

In a further embodiment, the metrology system 100 is a measurementsystem 100 that includes one or more computing systems 130 configured toexecute an automated measurement library control parameter optimization(AMLCPO) tool in accordance with the description provided herein. In thepreferred embodiment, the AMLCPO tool is a set of program instructions134 stored in a memory (e.g., memory 132 or an external memory). Theprogram instructions 134 are read and executed by one or more processorsof computing system 130 to realize library control parameteroptimization functionality as described herein. Computing system 130 maybe communicatively coupled to the spectrometer 104. In one aspect,computing system 130 is configured to receive measurement data 111associated with a measurement (e.g., critical dimension, film thickness,composition, process, etc.) of the structure 114 of specimen 112. In oneexample, the measurement data 111 includes an indication of the measuredspectral response of the specimen by measurement system 100 based on theone or more sampling processes from the spectrometer 104. In someembodiments, computing system 130 is further configured to determinespecimen parameter values of structure 114 from measurement data 111. Inone example, the computing system 130 is configured to access one ormore measurement libraries of pre-computed models for determining avalue of at least one specimen parameter value associated with thetarget structure 114. In some examples, the measurement libraries arestored in memory 132.

Computing system 130 is configured to receive reference measurement data113 from a reference measurement source 103. In some embodiments, thereference measurement source is any trusted measurement instrument, suchas a transmission electron microscope, a scanning electron microscope,an atomic force microscope, a scanning tunneling microscope, an x-raybased metrology system, etc., employed to measure one or more parametersof interest of the structure 114 of specimen 112. In some embodiments,the reference measurement source is any trusted measurement model, suchas a computational model that is sufficiently accurate, but toocomputationally burdensome for use in the course of high-throughputmetrology. The reference measurement data combined with the estimatedvalues of the same parameters of interest determined by library-basedmetrology system 100 provide the input data required for library controlparameter optimization. In addition, in some embodiments, computingsystem 130 is further configured to receive user input 117 from a userinput source 116 such as a graphical user interface, keyboard, etc. Insome embodiments, user input 117 includes an indication of theparameters of interest selected by the user to form the basis of thelibrary control parameter optimization. For example, a user may interactwith a graphical user interface (GUI) that allows the user to select aparticular critical dimension as the parameter of interest. Based on anindication of this particular critical dimension, computing system 130performs an optimization of the library control parameters that resultsin an optimal match between reference measurements of the particularcritical dimension and estimated values of the same critical dimensiondetermined by the library-based metrology system.

In some embodiments, measurement system 100 is further configured tostore one or more optimized library control parameter values 115 in amemory (e.g., memory 132 or an external memory).

It should be recognized that the various steps described throughout thepresent disclosure may be carried out by a single computer system 130or, alternatively, a multiple computer system 130. Moreover, differentsubsystems of the system 100, such as the spectroscopic ellipsometer101, may include a computer system suitable for carrying out at least aportion of the steps described herein. Therefore, the aforementioneddescription should not be interpreted as a limitation on the presentinvention but merely an illustration. Further, computing system 130 maybe configured to perform any other step(s) of any of the methodembodiments described herein.

The computing system 130 may include, but is not limited to, a personalcomputer system, mainframe computer system, workstation, image computer,parallel processor, or any other device known in the art. In general,the term “computing system” may be broadly defined to encompass anydevice having one or more processors, which execute instructions from amemory medium. In general, computing system 130 may be integrated with ameasurement system such as measurement system 100, or alternatively, maybe separate from any measurement system. In this sense, computing system130 may be remotely located and receive measurement data, referencemeasurement data 113, and user input 117 from any measurement source,reference measurement source, and user input source, respectively.

Program instructions 134 implementing methods such as those describedherein may be transmitted over a transmission medium such as a wire,cable, or wireless transmission link. Memory 132 storing programinstructions 134 may include a computer-readable medium such as aread-only memory, a random access memory, a magnetic or optical disk, ora magnetic tape.

In addition, the computer system 130 may be communicatively coupled tothe spectrometer 104 or the illuminator subsystem 102 of theellipsometer 101, or the user input source 103 in any manner known inthe art.

The computing system 130 may be configured to receive and/or acquiredata or information from the user input source 103 and subsystems of thesystem (e.g., spectrometer 104, illuminator 102, and the like) by atransmission medium that may include wireline and/or wireless portions.In this manner, the transmission medium may serve as a data link betweenthe computer system 130, user input source 103, and other subsystems ofthe system 100. Further, the computing system 130 may be configured toreceive measurement data via a storage medium (i.e., memory). Forinstance, the spectral results obtained using a spectrometer ofellipsometer 101 may be stored in a permanent or semi-permanent memorydevice (not shown). In this regard, the spectral results may be importedfrom an external system. Moreover, the computer system 130 may send datato external systems via a transmission medium.

The embodiments of the system 100 illustrated in FIG. 1 may be furtherconfigured as described herein. In addition, the system 100 may beconfigured to perform any other block(s) of any of the methodembodiment(s) described herein.

In general, ellipsometry is an indirect method of measuring physicalproperties of the specimen under inspection. In most cases, the measuredvalues (e.g., α_(meas) and β_(meas)) cannot be used to directlydetermine the physical properties of the specimen. The nominalmeasurement process consists of parameterization of the structure (e.g.,film thicknesses, critical dimensions, etc.) and the machine (e.g.,wavelengths, angles of incidence, polarization angles, etc.). Ameasurement model is created that attempts to predict the measuredvalues (e.g., α_(meas) and β_(meas)). As illustrated in equations (1)and (2), the measurement model includes parameters associated with themachine (P_(machine)) and the specimen (P_(specimen)).α_(model) =f(P _(machine) ,P _(specimen))  (1)β_(model) =g(P _(machine) ,P _(specimen))  (2)

Machine parameters are parameters used to characterize the metrologytool (e.g., ellipsometer 101). Exemplary machine parameters includeangle of incidence (AOI), analyzer angle (A₀), polarizer angle (P₀),illumination wavelength, numerical aperture (NA), etc. Specimenparameters are parameters used to characterize the specimen (e.g.,specimen 112 including structures 114). For a thin film specimen,exemplary specimen parameters include refractive index, dielectricfunction tensor, nominal layer thickness of all layers, layer sequence,etc. For measurement purposes, the machine parameters are treated asknown, fixed parameters and one or more of the specimen parameters aretreated as unknown, floating parameters.

In some examples, the floating parameters are resolved by an iterativeprocess (e.g., regression) that produces the best fit betweentheoretical predictions provided by a measurement library andexperimental data. The unknown specimen parameters, P_(specimen), arevaried and the model output values (e.g., α_(model) and β_(model)) areestimated until a set of specimen parameter values are determined thatresults in a close match between the model output values and theexperimentally measured values (e.g., α_(meas) and β_(meas)). In someexamples, the floating parameters are resolved by a search through alibrary of pre-computed solutions to find the closest match. In a modelbased measurement application such as spectroscopic ellipsometry on a CDspecimen, a library search process is employed to identify specimenparameter values that minimize the differences between pre-computedoutput values and the experimentally measured values for a fixed set ofmachine parameter values.

In a library-based measurement application, the selection of librarycontrol parameters affects the accuracy of measurement results. In someembodiments, the library control parameters include measurementsubsystem combination weights, measurement signal weights, one or morespecimen parameters fixed to specific values, one or more constraints onfloating parameter values, or any combination thereof.

In some examples, a particular metrology target is subjected tomeasurement by multiple, different measurement subsystems. Measurementdata is collected from each of the multiple, different measurementsubsystems. Relative weights are applied to the measurement datacollected by each different measurement subsystem. The weightedmeasurement data is processed by the measurement library, or combinationof measurement libraries to arrive at an estimated value of a parameterof interest. In another example, a measurement system generatesmultiple, different measurement signals associated with a measurement ofa particular metrology target. Relative weights are applied to eachdifferent measurement signal generated by each measurement system. Theweighted measurement signal data is processed by the measurementlibrary, or combination of measurement libraries to arrive at anestimated value of a parameter of interest. In another example, one ormore of the floating parameters resolved by the measurement library(e.g., one or more of the parameters, P_(specimen), illustrated inequations (1) and (2)) is set to a fixed value during measurement. Inyet another example, one or more of the floating parameters resolved bythe measurement library is constrained during measurement. In oneexample, a functional relationship is established between two floatingparameters (e.g., P_(specimen1)=f(P_(specimen2))). Thus, the values ofthe two input parameters are constrained by the functional relationshipduring the library search phase of the measurement.

FIG. 2 is a diagram illustrative of an exemplary AMLCPO tool 150implemented by computing system 130. In the embodiment depicted in FIG.2, computing system 130 is configured to implement automated librarycontrol parameter optimization functionality as described herein.

In the embodiment depicted in FIG. 2, AMLCPO tool 150 includes aprecomputed measurement library 152 and a library control optimizationmodule 151. AMLCPO tool 150 receives an indication 141 of one or moreparameters of interest selected by a user 140 (e.g., a particularcritical dimension of a metrology target under measurement). Precomputedmeasurement library 152 receives measured signals 154 (e.g., measuredspectra) associated with a measurement of a particular metrology target(e.g., a structure 114 fabricated on specimen 112) by a targetmeasurement system (e.g., metrology system 100). The precomputedmeasurement library 152 estimates values of the selected parameter ofinterest (e.g., the critical dimension parameter selected by the user140) based on the measured signals 154 and a predetermined (e.g.,default) set of library control parameter values. Precomputedmeasurement library 152 communicates an indication 155 of the estimatedvalues of the selected parameter of interest to the library controloptimization module 151. The library control optimization module 151also receives an indication 153 of the values of the selected parametersof interest as measured by a reference measurement system. The referencemeasurement system performs measurements of the same metrology targetsas the target measurement system. Library control optimization moduledetermines a new set of library control parameter values based on thereference measurements 153 of the selected parameters of interest andthe estimated values of the selected parameters of interest 155. Anindication 156 of the new set of library control parameters iscommunicated from library control optimization module 151 to theprecomputed measurement library 152. The precomputed measurement library152 estimates values of the selected parameter of interest based on themeasured signals 154 and the new set of library control parametervalues. The updated values of the selected parameters of interest arecommunicated to library control optimization module 151. Precomputedmeasurement library 152 communicates an indication 155 of the estimatedvalues of the selected parameter of interest to the library controloptimization module 151. Library control optimization module determinesanother new set of library control parameter values based on thereference measurements 153 of the selected parameters of interest andthe estimated values of the selected parameters of interest 155. Thisprocess is iterated until a satisfactory match between the referencemeasurements 153 of the selected parameters of interest and theestimated values of the selected parameters of interest is achieved.

An indication 157 of the set of library control parameter values thatachieves a satisfactory match is stored in a memory (e.g., memory 160).Subsequent measurements of similar metrology targets may be performed bythe target measurement system using the precomputed measurement library152 with the optimized set of library control parameters. Suchmeasurements may be employed as part of a high-throughput, in-linemetrology tool. Alternatively, the measurements may be employed as partof the modeling and design of metrology systems, the modeling and designof metrology targets, or both.

Library control optimization module 151 searches for library controlparameter values such that the library-based measurement of userselected parameters of interest closely matches the value of theseparameters of interest as measured by a trusted reference measurementsystem.

In some embodiments, the cost function for the optimization is definedas a least squares error of one or more metrics that characterize thefit between reference data and corresponding library-based measurementdata. In one example, the fit is characterized by the slope and R²values corresponding to the fit between reference data and correspondinglibrary-based measurement data. Equation (3) illustrates an exemplarycost function including both metrics.

$\begin{matrix}{{CostFuncion} = {{\sum\limits_{i = 0}^{N}\left( {1 - R_{{POI}_{i}}^{2}} \right)^{2}} + {\sum\limits_{i = 0}^{N}\left( {1 - {Slope}_{{POI}_{i}}} \right)^{2}}}} & (3)\end{matrix}$

In one example, a maximum likelihood estimation is employed to optimizethe library control parameters. In this example, library controloptimization module 151 characterizes the fitting quality by evaluatingthe cost function illustrated by equation (3).

FIG. 3 depicts an illustrative plot 165 of estimated values of aparameter of interest (POI) (e.g., values 155 depicted in FIG. 2) andcorresponding values of the parameter of interest as measured by areference measurement system (e.g., values 153 depicted in FIG. 2). Ifthe estimated values of the parameter of interest perfectly matched thecorresponding known values, all points would lie on line 167. Inreality, there are discrepancies. Line 166 represents a linear fit tothe data points.

In some examples, library control optimization module 151 determines theslope of the regression line of the data points (e.g., line 166 depictedin FIG. 3).

In some examples, library control optimization module 151 determines theR² value (i.e., coefficient of determination) associated with thedifferences between the estimated values of the parameter of interestand the known values of the parameter of interest. The range of R²values is between zero and one, with one being a perfect fit between theestimated values of the parameter of interest and the known values ofthe parameter of interest for each measurement. In some examples, the R²value is calculated as illustrated in equation (6).

$\begin{matrix}{R^{2} = {1 - \frac{\sum\limits_{i = 1}^{N}e_{i}^{2}}{\frac{1}{N}{\sum\limits_{i = 1}^{N}y_{{est}_{i}}}}}} & (4)\end{matrix}$

The estimated value of the parameter of interest is denoted a y_(est)_(i) and the reference value of the parameter of interest is denoted asy_(known) _(i) , and e_(i) is defined by equation (5).e _(i) =y _(est) _(i) −y _(known) _(i)   (5)

In this example, library control optimization module 151 perturbs eachlibrary control parameter to be optimized and calculates the numericalJacobian of the residue with respect to each library control parameterto be optimized. The determined sensitivities are employed by librarycontrol optimization module 151 to determine an updated value of eachlibrary control parameter to be optimized. Various methods may beemployed to update the parameter values. By way of non-limiting example,any of the Levenberg-Marquardt method, the gradient decent method, theGaussian-Newton methods, etc., may be employed by library controloptimization module 151.

The updating of the library control parameter values is performediteratively until a stop condition is achieved. In one example, a stopcondition is achieved when measurement accuracy, defined as the 3σ valueof the difference between the estimated value of the parameter ofinterest and the reference value of the parameter of interest, reaches apredetermined threshold value. In one example, accuracy is defined byequation (6), where the mean value of differences between the estimatedvalues and reference values is defined by equation (7).

$\begin{matrix}{{Accuracy} = {{3\;\sigma} = {3\sqrt{{\frac{1}{N}{\sum\limits_{i = 1}^{N}e_{i}}} - \overset{\_}{e}}}}} & (6) \\{\overset{\_}{e} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}e_{i}}}} & (7)\end{matrix}$

In general, any number of parameters of interest may be selected andprovide the basis for library control parameter optimization. Exemplaryparameters of interest include geometric parameters such as a shapeparameter such as a critical dimension (CD), sidewall angle (SWA),height (H), etc., composition, film thickness, bandgap, electricalproperties, lithography focus, lithography dosage, overlay, and otherprocess parameters (e.g., resist state, partial pressure, temperature,focusing model).

In general, any one, or combination, of library control parameters maybe subject to optimization. Thus, measurement subsystem combinationweights, measurement signal weights, fixed parameter values, parameterconstraints, or any combination thereof may be optimized. Moreover, theoptimization of each library control parameter may be conductedindependently or together in a cascaded optimization framework.

For illustrative purposes, FIG. 4 depicts a metrology target 170 to bemeasured. Geometric parameters of interest include critical dimension(CD) offsets A-E. CD offset A is the difference between criticaldimension, A, and trench bottom critical dimension, BCD, depicted inFIG. 4. Similarly, CD offset B is the difference between criticaldimension, B, and trench bottom critical dimension, BCD, depicted inFIG. 4, etc. CD offsets A-E are similar and difficult to be measure. Acombination of different spectroscopic ellipsometer and reflectometertechniques are employed to measure these parameters of interest.

In one example, four different measurement system combinations areemployed to measure the CD offsets A-E. The measurement systemcombinations are a rotating polarizer spectroscopic ellipsometer at anazimuth angle of zero degrees, a rotating polarizer spectroscopicellipsometer at an azimuth angle of ninety degrees, a laser drivenspectroscopic reflectometer at a polarizer angle of zero degrees, and alaser driven spectroscopic reflectometer at a polarizer angle of ninetydegrees.

FIGS. 5A-5C depict tables 171-173, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for ten different weightingsamong the four different measurement system combinations described inthis example. Table 171 indicates the fitting quality (i.e., R² andslope) between the reference data and the library-based measurement forCD offset A and CD offset B. Table 172 indicates the fitting quality(i.e., R² and slope) between the reference data and the library-basedmeasurement for CD offset C and CD offset D. Table 173 indicates thefitting quality (i.e., R² and slope) between the reference data and thelibrary-based measurement for CD offset E and the average goodness offit (i.e., Chi² value) associated with CD offsets A-E for each differentweighting.

As illustrated in FIGS. 5A-5B, each fit associated with CD offsets B-Dis quite poor when an equal weighting is applied across all fourmeasurement subsystems. The AMLCPO tool 150 is iteratively applied toautomatically recommend improved measurement subsystem weightingparameters. As illustrated in FIGS. 5A-5C, the fitting quality improvessignificantly and the average Chi² value is reduced the measurementsubsystem weights are evolved in the manner described herein.

In another example, three different measurement system combinations areemployed to measure the CD offsets A-E. The measurement systemcombinations are a laser driven spectroscopic reflectometer at apolarizer angle of zero degrees, a laser driven spectroscopicreflectometer at a polarizer angle of ninety degrees, and a rotatingpolarizer, rotating compensator spectroscopic ellipsometer at an azimuthangle of forty-five degrees.

FIGS. 6A-6C depict tables 174-176, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for eleven differentweightings among the three different measurement system combinationsdescribed in this example. Table 174 indicates the fitting quality(i.e., R² and slope) between the reference data and the library-basedmeasurement for CD offset A and CD offset B. Table 175 indicates thefitting quality (i.e., R² and slope) between the reference data and thelibrary-based measurement for CD offset C and CD offset D. Table 176indicates the fitting quality (i.e., R² and slope) between the referencedata and the library-based measurement for CD offset E and the averagegoodness of fit (i.e., Chi² value) associated with CD offsets A-E foreach different weighting.

As illustrated in FIGS. 6A-6B, each fit associated with CD offsets B-Dis quite poor when an equal weighting is applied across all threemeasurement subsystems. The AMLCPO tool 150 is iteratively applied toautomatically recommend improved measurement subsystem weightingparameters. As illustrated in FIGS. 6A-6C, the fitting quality improvessignificantly and the average Chi² value is reduced the measurementsubsystem weights are evolved in the manner described herein.

In yet another example, two different measurement system combinationsare employed to measure the CD offsets A-E. The measurement systemcombinations are a laser driven spectroscopic reflectometer at apolarizer angle of zero degrees and a laser driven spectroscopicreflectometer at a polarizer angle of ninety degrees.

FIGS. 7A-7C depict tables 177-179, indicative of the differences betweenreference data associated with CD offsets A-E and values of CD offsetsA-E estimated by library-based measurement for eight differentweightings among the two different measurement system combinationsdescribed in this example. Table 177 indicates the fitting quality(i.e., R² and slope) between the reference data and the library-basedmeasurement for CD offset A and CD offset B. Table 178 indicates thefitting quality (i.e., R² and slope) between the reference data and thelibrary-based measurement for CD offset C and CD offset D. Table 179indicates the fitting quality (i.e., R² and slope) between the referencedata and the library-based measurement for CD offset E and the averagegoodness of fit (i.e., Chi² value) associated with CD offsets A-E foreach different weighting.

As illustrated in FIGS. 7A-7B, each fit associated with CD offsets B-Dshows very poor sensitivity when an equal weighting is applied acrossboth measurement subsystems. The AMLCPO tool 150 is iteratively appliedto automatically recommend improved measurement subsystem weightingparameters. As illustrated in FIGS. 7A-7C, the fitting quality improvessignificantly and the average Chi² value is reduced the measurementsubsystem weights are evolved in the manner described herein. Forexample, the R² value associated with the measurement of CD offset Cimproves from 0.023 to 0.939 at iteration number six. Similarly, theslope improves from 0.367 to 1.006 at iteration number six.

FIG. 8 illustrates a method 200 for optimizing a set of measurementlibrary control parameters for a particular metrology application in atleast one novel aspect. Method 200 is suitable for implementation by ametrology system such as metrology system 100 illustrated in FIG. 1 ofthe present invention. In one aspect, it is recognized that dataprocessing blocks of method 200 may be carried out via a pre-programmedalgorithm executed by one or more processors of computing system 130, orany other general purpose computing system. It is recognized herein thatthe particular structural aspects of metrology system 100 do notrepresent limitations and should be interpreted as illustrative only.

In block 201, a plurality of measurement signals associated withmeasurements of one or more metrology targets disposed on a wafer arereceived by a computing system (e.g., computing system 130). Themeasurement signals are associated with measurements performed in one ormore measurement system configurations.

In block 202, an amount of reference measurement data indicative ofreference values of one or more parameters of interest of the one ormore metrology targets disposed on the wafer is received by a computingsystem (e.g., computing system 130).

In block 203, values of the one or more parameters of interest of theone or more metrology targets disposed on the wafer are estimated basedon a fitting of a pre-computed measurement library function to themeasurement signals. The pre-computed measurement library is controlledby a default set of library control parameter values for purposes ofestimating the values of the one or more parameters of interest of theone or more metrology targets disposed on the wafer.

In block 204, one or more of the library control parameters areoptimized to minimize differences between the reference data and thevalues of the one or more parameters of interest estimated based on thefitting of the pre-computed measurement library function to themeasurement signals. The optimization is performed without recalculatingthe pre-computed measurement library function.

In an optional block (not shown), the optimized library controlparameters are stored in a memory of a computing system (e.g., memory132 of computing system 130 or an external memory).

Although the methods discussed herein are explained with reference tosystem 100, any library based metrology system configured to illuminateand detect light reflected, transmitted, or diffracted from a specimenmay be employed to implement the exemplary methods described herein.Exemplary systems include an angle-resolved reflectometer, ascatterometer, a reflectometer, an ellipsometer, a spectroscopicreflectometer or ellipsometer, a beam profile reflectometer, amulti-wavelength, two-dimensional beam profile reflectometer, amulti-wavelength, two-dimensional beam profile ellipsometer, a rotatingcompensator spectroscopic ellipsometer, etc. By way of non-limitingexample, an ellipsometer may include a single rotating compensator,multiple rotating compensators, a rotating polarizer, a rotatinganalyzer, a modulating element, multiple modulating elements, or nomodulating element.

It is noted that the output from a reference source and/or targetmeasurement system may be configured in such a way that the measurementsystem uses more than one technology. In fact, an application may beconfigured to employ any combination of available metrology sub-systemswithin a single tool, or across a number of different tools.

A system implementing the methods described herein may also beconfigured in a number of different ways. For example, a wide range ofwavelengths (including visible, ultraviolet, infrared, and X-ray),angles of incidence, states of polarization, and states of coherence maybe contemplated. In another example, the system may include any of anumber of different light sources (e.g., a directly coupled lightsource, a laser-sustained plasma light source, etc.). In anotherexample, the system may include elements to condition light directed toor collected from the specimen (e.g., apodizers, filters, etc.).

The invention presented herein addresses the problem of determiningoptimal library control parameters for a particular measurementapplication. In many cases, this problem is intractable without the aidof the methods and systems described herein. Moreover, the methoddescribed in this invention is not limited to the hardware and/oroptical configuration summarized above.

In the field of semiconductor metrology, a metrology system may comprisean illumination system which illuminates a target, a collection systemwhich captures relevant information provided by the illuminationsystem's interaction (or lack thereof) with a target, device or feature,and a processing system which analyzes the information collected usingone or more algorithms. Metrology tools can be used to measurestructural and material characteristics (e.g, material composition,dimensional characteristics of structures and films such as filmthickness and/or critical dimensions of structures, overlay, etc.)associated with various semiconductor fabrication processes. Thesemeasurements are used to facilitate process controls and/or yieldefficiencies in the manufacture of semiconductor dies.

A metrology system can comprise one or more hardware configurationswhich may be used in conjunction with certain embodiments of thisinvention to, e.g., measure the various aforementioned semiconductorstructural and material characteristics. Examples of such hardwareconfigurations include, but are not limited to, the following: aspectroscopic ellipsometer (SE), a SE with multiple angles ofillumination, a SE measuring Mueller matrix elements (e.g. usingrotating compensator(s)), a single-wavelength ellipsometer, a beamprofile ellipsometer (angle-resolved ellipsometer), a beam profilereflectometer (angle-resolved reflectometer), a broadband reflectivespectrometer (spectroscopic reflectometer), a single-wavelengthreflectometer, an angle-resolved reflectometer, an imaging system, and ascatterometer (e.g. speckle analyzer).

The hardware configurations can be separated into discrete operationalsystems. On the other hand, one or more hardware configurations can becombined into a single tool. One example of such a combination ofmultiple hardware configurations into a single tool is described in U.S.Pat. No. 7,933,026, which is hereby incorporated by reference in itsentirety for all purposes. In many cases, multiple metrology tools areused for measurements on single or multiple metrology targets. This isdescribed, e.g. in by Zangooie et al., in U.S. Pat. No. 7,478,019, whichis hereby incorporated by reference in its entirety for all purposes.

As described herein, the term “critical dimension” includes any criticaldimension of a structure (e.g., bottom critical dimension, middlecritical dimension, top critical dimension, sidewall angle, gratingheight, etc.), a critical dimension between any two or more structures(e.g., distance between two structures), a displacement between two ormore structures (e.g., overlay displacement between overlaying gratingstructures, etc.), and a dispersion property value of a material used inthe structure or part of the structure. Structures may include threedimensional structures, patterned structures, overlay structures, etc.

As described herein, the term “critical dimension application” or“critical dimension measurement application” includes any criticaldimension measurement.

As described herein, the term “metrology system” includes anymeasurement system employed at least in part to characterize a specimenin any aspect, including systems that may be referred to as “inspection”systems. Such terms of art do not limit the scope of the term “metrologysystem” as described herein. In addition, the metrology system 100 maybe configured for measurement of patterned wafers and/or unpatternedwafers. The metrology system may be configured as a LED inspection tool,edge inspection tool, backside inspection tool, macro-inspection tool,or multi-mode inspection tool (involving data from one or more platformssimultaneously), and any other metrology or inspection tool thatbenefits from the calibration of system parameters based on criticaldimension data.

Various embodiments are described herein for a semiconductor processingsystem (e.g., a metrology system or a lithography system) that may beused for processing a specimen. The term “specimen” is used herein torefer to a site, or sites, on a wafer, a reticle, or any other samplethat may be processed (e.g., printed or inspected for defects) by meansknown in the art. In some examples, the specimen includes a single sitehaving one or more measurement targets whose simultaneous, combinedmeasurement is treated as a single specimen measurement or referencemeasurement. In some other examples, the specimen is an aggregation ofsites where the measurement data associated with the aggregatedmeasurement site is a statistical aggregation of data associated witheach of the multiple sites. Moreover, each of these multiple sites mayinclude one or more measurement targets associated with a specimen orreference measurement.

As used herein, the term “wafer” generally refers to substrates formedof a semiconductor or non-semiconductor material. Examples include, butare not limited to, monocrystalline silicon, gallium arsenide, andindium phosphide. Such substrates may be commonly found and/or processedin semiconductor fabrication facilities. In some cases, a wafer mayinclude only the substrate (i.e., bare wafer). Alternatively, a wafermay include one or more layers of different materials formed upon asubstrate. One or more layers formed on a wafer may be “patterned” or“unpatterned”. For example, a wafer may include a plurality of dieshaving repeatable pattern features.

A “reticle” may be a reticle at any stage of a reticle fabricationprocess, or a completed reticle that may or may not be released for usein a semiconductor fabrication facility. A reticle, or a “mask,” isgenerally defined as a substantially transparent substrate havingsubstantially opaque regions formed thereon and configured in a pattern.The substrate may include, for example, a glass material such asamorphous SiO₂. A reticle may be disposed above a resist-covered waferduring an exposure step of a lithography process such that the patternon the reticle may be transferred to the resist.

One or more layers formed on a wafer may be patterned or unpatterned.For example, a wafer may include a plurality of dies, each havingrepeatable pattern features. Formation and processing of such layers ofmaterial may ultimately result in completed devices. Many differenttypes of devices may be formed on a wafer, and the term wafer as usedherein is intended to encompass a wafer on which any type of deviceknown in the art is being fabricated.

In one or more exemplary embodiments, the functions described may beimplemented in hardware, software, firmware, or any combination thereof.If implemented in software, the functions may be stored on ortransmitted over as one or more instructions or code on acomputer-readable medium. Computer-readable media includes both computerstorage media and communication media including any medium thatfacilitates transfer of a computer program from one place to another. Astorage media may be any available media that can be accessed by ageneral purpose or special purpose computer. By way of example, and notlimitation, such computer-readable media can comprise RAM, ROM, EEPROM,CD-ROM or other optical disk storage, magnetic disk storage or othermagnetic storage devices, or any other medium that can be used to carryor store desired program code means in the form of instructions or datastructures and that can be accessed by a general-purpose orspecial-purpose computer, or a general-purpose or special-purposeprocessor. Also, any connection is properly termed a computer-readablemedium. For example, if the software is transmitted from a website,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition of medium.Disk and disc, as used herein, includes compact disc (CD), laser disc,optical disc, digital versatile disc (DVD), floppy disk and blu-ray discwhere disks usually reproduce data magnetically, while discs reproducedata optically with lasers. Combinations of the above should also beincluded within the scope of computer-readable media.

Although certain specific embodiments are described above forinstructional purposes, the teachings of this patent document havegeneral applicability and are not limited to the specific embodimentsdescribed above. Accordingly, various modifications, adaptations, andcombinations of various features of the described embodiments can bepracticed without departing from the scope of the invention as set forthin the claims.

What is claimed is:
 1. A metrology system comprising: one or moreillumination sources configured to provide an amount of illuminationlight to a first set of one or more metrology targets in accordance withone or more different measurement system configurations; one or moredetectors configured to receive an amount of collected light from theone or more metrology targets in response to the amount of illuminationlight in accordance with the one or more measurement systemconfigurations and generate measurement signals indicative of thecollected light associated with each of the one or more measurementsystem configurations; and one or more computer systems configured to:receive the measurement signals associated with each of the one or moremeasurement system configurations; receive an amount of referencemeasurement data indicative of reference values of one or moreparameters of interest of the first set of one or more metrologytargets; estimate values of the one or more parameters of interest ofthe first set of one or more metrology targets based on a fitting of apre-computed measurement library function to the measurement signalsusing a default set of library control parameter values; and optimizeone or more of the library control parameters to minimize differencesbetween the reference data and the values of the one or more parametersof interest estimated based on the fitting of the pre-computedmeasurement library function to the measurement signals, wherein theoptimizing is performed without recalculating the pre-computedmeasurement library function, the one or more illumination sources arefurther configured to provide a second amount of illumination light to asecond set of one or more metrology targets in accordance with the oneor more different measurement system configurations; the one or moredetectors are further configured to receive an amount of collected lightfrom the one or more metrology targets in response to the second amountof illumination light in accordance with the one or more measurementsystem configurations and generate a second plurality of measurementsignals indicative of the collected light associated with each of theone or more measurement system configurations; and wherein the one ormore computer systems are further configured to: receive the secondplurality of measurement signals associated with each of the one or moremeasurement system configurations; and estimate values of the one ormore parameters of interest of the second set of one or more metrologytargets based on a fitting of the pre-computed measurement libraryfunction to the second plurality of measurement signals using theoptimized library control parameter values.
 2. The metrology system ofclaim 1, wherein the first set of one or more metrology targets and thesecond set of metrology targets are the same set of one or moremetrology targets.
 3. The metrology system of claim 1, wherein thereference measurement data is received from a reference measurementsource that is different from the metrology system.
 4. The metrologysystem of claim 3, wherein the reference measurement source included anyof a transmission electron microscope, a scanning electron microscope,an atomic force microscope, a scanning tunneling microscope, an x-raybased metrology system, or any combination thereof.
 5. The metrologysystem of claim 1, wherein the pre-computed measurement library functionis a trained neural network model.
 6. The metrology system of claim 1,wherein the optimizing of the one or more library control parametersinvolves minimizing a cost function comprising a least squares error ofone or more metrics characterizing a fit between the referencemeasurement data and corresponding values of the one or more parametersof interest estimated based on the fitting of the pre-computedmeasurement library function to the measurement signals.
 7. Themetrology system of claim 1, wherein the library control parametersinclude a plurality of measurement subsystem combination weights, aplurality of measurement signal weights, one or more specimen parametersfixed to specific values, and one or more constraints on floatingparameter values.
 8. The metrology system of claim 1, wherein the one ormore measurement system configurations includes any of a spectroscopicellipsometer configuration, a spectroscopic reflectometer configuration,a single-wavelength ellipsometer configuration, a single wavelengthreflectometer configuration, a beam profile ellipsometer configuration,and a beam profile reflectometer configuration.
 9. The metrology systemof claim 1, wherein the parameters of interest include any of a shapeparameter, stress, a material composition, lithography focus,lithography dosage, and overlay.
 10. An Automated Measurement LibraryControl Parameter Optimization (AMLCPO) tool comprisingcomputer-readable instructions stored on a non-transitory,computer-readable medium, the computer-readable instructions comprising:code for causing a computing system to receive a plurality ofmeasurement signals associated with measurements of a first set of oneor more metrology targets in one or more measurement systemconfigurations; code for causing the computing system to receive anamount of reference measurement data indicative of reference values ofone or more parameters of interest of the first set of one or moremetrology targets; code for causing the computing system to estimatevalues of the one or more parameters of interest of the first set of oneor more metrology targets based on a fitting of a pre-computedmeasurement library function to the measurement signals using a defaultset of library control parameter values; code for causing the computingsystem to optimize one or more of the library control parameters tominimize differences between the reference data and the values of theone or more parameters of interest estimated based on the fitting of thepre-computed measurement library function to the measurement signals,wherein the optimizing is performed without recalculating thepre-computed measurement library function; code for causing thecomputing system to receive a second plurality of measurement signalsassociated with measurements of a second set of one or more metrologytargets in the one or more measurement system configurations; and codefor causing the computing system to estimate values of the one or moreparameters of interest of the second set of one or more metrologytargets based on a fitting of the pre-computed measurement libraryfunction to the second plurality of measurement signals using theoptimized library control parameter values.
 11. The AMLCPO tool of claim10, wherein the first set of one or more metrology targets and thesecond set of metrology targets are the same set of one or moremetrology targets.
 12. The AMLCPO tool of claim 10, wherein thereference measurement data is received from a reference measurementsource that is different from the metrology system.
 13. The AMLCPO toolof claim 10, wherein the optimizing of the one or more library controlparameters involves minimizing a cost function comprising a leastsquares error of one or more metrics characterizing a fit between thereference measurement data and corresponding values of the one or moreparameters of interest estimated based on the fitting of thepre-computed measurement library function to the measurement signals.14. The AMLCPO tool of claim 10, wherein the library control parametersinclude a plurality of measurement subsystem combination weights, aplurality of measurement signal weights, one or more specimen parametersfixed to specific values, and one or more constraints on floatingparameter values.
 15. The AMLCPO tool of claim 10, wherein the one ormore measurement system configurations includes any of a spectroscopicellipsometer configuration, a spectroscopic reflectometer configuration,a single-wavelength ellipsometer configuration, a single wavelengthreflectometer configuration, a beam profile ellipsometer configuration,and a beam profile reflectometer configuration.
 16. The metrology systemof claim 10, wherein the parameters of interest include any of a shapeparameter, stress, a material composition, lithography focus,lithography dosage, and overlay.
 17. A method comprising: receiving aplurality of measurement signals associated with measurements of a firstset of one or more metrology targets in one or more measurement systemconfigurations; receiving an amount of reference measurement dataindicative of reference values of one or more parameters of interest ofthe first set of one or more metrology targets; estimating values of theone or more parameters of interest of the first set of one or moremetrology targets based on a fitting of a pre-computed measurementlibrary function to the measurement signals using a default set oflibrary control parameter values; and optimizing one or more of thelibrary control parameters to minimize differences between the referencedata and the values of the one or more parameters of interest estimatedbased on the fitting of the pre-computed measurement library function tothe measurement signals, wherein the optimizing is performed withoutrecalculating the pre-computed measurement library function; receiving asecond plurality of measurement signals associated with measurements ofa second set of one or more metrology targets in the one or moremeasurement system configurations; and estimating values of the one ormore parameters of interest of the second set of one or more metrologytargets based on a fitting of the pre-computed measurement libraryfunction to the second plurality of measurement signals using theoptimized library control parameter values.
 18. The method of claim 17,wherein the first set of one or more metrology targets and the secondset of metrology targets are the same set of one or more metrologytargets.
 19. The method of claim 17, wherein the library controlparameters include a plurality of measurement subsystem combinationweights, a plurality of measurement signal weights, one or more specimenparameters fixed to specific values, and one or more constraints onfloating parameter values.
 20. The method of claim 17, wherein the oneor more measurement system configurations includes any of aspectroscopic ellipsometer configuration, a spectroscopic reflectometerconfiguration, a single-wavelength ellipsometer configuration, a singlewavelength reflectometer configuration, a beam profile ellipsometerconfiguration, and a beam profile reflectometer configuration.